𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems

✍ Scribed by Maciej Błaszak; Wen-Xiu Ma

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
176 KB
Volume
47
Category
Article
ISSN
0393-0440

No coin nor oath required. For personal study only.

✦ Synopsis

A systematic construction of Stäckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One-Casimir bi-Hamiltonian case is studied in details and in this case, a systematic construction of related hydrodynamic systems in arbitrary coordinates is presented, using the cofactor method and soliton symmetry constraints.

📜 SIMILAR VOLUMES

Separable Hamiltonians and integrable sy
Separable Hamiltonians and integrable systems of hydrodynamic type
✍ E.V. Ferapontov; A.P. Fordy 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 545 KB

We exhibit a surprising relationship between separable Hamiltonians and integrable, linearly degenerate systems of hydrodynamic type. This gives a new way of obtaining the general solution of the latter. Our formulae also lead to interesting canonical transformations between large classes of St~icke

On the connection between Hamiltonian ma
On the connection between Hamiltonian many-particle systems and the hydrodynamical equations
✍ Karl Oelschläger 📂 Article 📅 1991 🏛 Springer 🌐 English ⚖ 564 KB

We consider certain Hamiltonian systems with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical processes of the positions and the velocities respectively converge to solutions of